Mean field limits for charged particles

The aim of this thesis is to provide a rigorous mathematical derivation of the Vlasov-Poisson equation and the Vlasov-Maxwell equations in the large N limit of interacting charged particles. We will extend a method previously proposed by Boers and Pickl to perform a mean field limit for the Vlasov-Poisson equation with the full Coulomb singularity and an N-dependent cut-off decreasing as $N^{-1/3 + \epsilon}$. We will then discuss an alternative approach, deriving the Vlasov-Poisson equation as a combined mean field and point-particle limit of an N-particle Coulomb system of extended charges. Finally, we will combine both methods to prove a mean field limit for the relativistic Vlasov-Maxwell system in 3+1 dimensions. In each case, convergence of the empirical measures to solutions of the corresponding mean field equation can be shown for typical initial conditions. This implies, in particular, the propagation of chaos for the respective dynamics.

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Mean field limits for charged particles is an episode from Fakultät für Mathematik, Informatik und Statistik - Digitale Hochschulschriften der LMU - Teil 02/02 by Ludwig-Maximilians-Universität München.

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This episode was published on Dec 21, 2015.

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